javascript - 添加到 Number.MAX_VALUE

Question

这个问题的答案可能非常明显，但我无法在 Mozilla 文档或 Google 上粗略搜索找到它。

如果你有这样的代码

Number.MAX_VALUE + 1; // Infinity, right?
Number.MIN_VALUE - 1; // -Infinity, right?

然后我希望将 任何东西 添加到 Number.MAX_VALUE 会将它推到 Infinity。结果只是 Number.MAX_VALUE 向我吐口水。

但是，当我在 Chrome JS 控制台中玩游戏时，我注意到它实际上并没有变成 Infinity 直到我添加/减去足够多:

Number.MAX_VALUE + Math.pow(100,1000); // now we hit Infinity
Number.MIN_VALUE - Math.pow(100,1000); // -Infinity at last

Number.MAX_VALUE 和 Infinity 之间的这个“缓冲区”的解释是什么？

Answer 1

标准...

在 ECMAScript 中，两个非零有限数的加法实现为_{^{(ECMA-262 §11.6.3 "Applying the Additive Operators to Numbers")}}:

the sum is computed and rounded to the nearest representable value using IEEE 754 round-to-nearest mode. If the magnitude is too large to represent, the operation overflows and the result is then an infinity of appropriate sign.

IEEE-754 的舍入到最近模式指定_{^{(IEEE-754 2008 §4.3.1 "Rounding-direction attributes to nearest")}}

In the following two rounding-direction attributes, an infinitely precise result with magnitude at least b^emax ( b − ½ b^1-p ) shall round to ∞ with no change in sign; here emax and p are determined by the destination format (see 3.3). With:

• roundTiesToEven, the floating-point number nearest to the infinitely precise result shall be delivered; if the two nearest floating-point numbers bracketing an unrepresentable infinitely precise result are equally near, the one with an even least significant digit shall be delivered
• roundTiesToAway, the floating-point number nearest to the infinitely precise result shall be delivered; if the two nearest floating-point numbers bracketing an unrepresentable infinitely precise result are equally near, the one with larger magnitude shall be delivered.

ECMAScript 没有指定哪一个舍入到最近，但在这里并不重要，因为两者给出相同的结果。 ECMAScript中的数字是“double”，其中

• b = 2
• emax = 1023
• p = 53,

因此结果必须至少为 2¹⁰²⁴ - 2⁹⁷⁰ ~ 1.7976931348623158 × 10³⁰⁸ in为了四舍五入到无穷大。否则它会四舍五入到 MAX_VALUE，因为 比 Infinity 更接近。

注意 MAX_VALUE = 2¹⁰²⁴ - 2⁹⁷¹，所以你至少需要加上 2⁹⁷¹ - 2⁹⁷⁰ = 2⁹⁷⁰ ~ 9.979202 × 10²⁹¹ 以获得无穷大。我们可以检查:

>>> Number.MAX_VALUE + 9.979201e291
1.7976931348623157e+308
>>> Number.MAX_VALUE + 9.979202e291
Infinity

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与此同时，您的 Math.pow(100,1000) ~ 2^6643.9 远远超过 2¹⁰²⁴ - 2⁹⁷⁰。它已经是无穷大了。